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A180201 Inverse permutation to A180200.

%I A180201 #42 Mar 21 2025 20:31:23
%S A180201 0,1,2,3,5,4,6,7,11,10,8,9,13,12,14,15,23,22,20,21,17,16,18,19,27,26,
%T A180201 24,25,29,28,30,31,47,46,44,45,41,40,42,43,35,34,32,33,37,36,38,39,55,
%U A180201 54,52,53,49,48,50,51,59,58,56,57,61,60,62,63,95,94,92,93,89,88,90,91,83
%N A180201 Inverse permutation to A180200.
%C A180201 A180199(n) = a(a(n));
%C A180201 a(A180198(n)) = A180198(a(n)) = A180200(n);
%C A180201 a(A075427(n)) = A075427(n).
%C A180201 This permutation transforms the enumeration system of positive irreducible fractions A245325/A245326 into the enumeration system A007305/A047679 (Stern-Brocot), and enumeration system A071766/A229742 (HCS) into A162909/A162910 (Bird). - _Yosu Yurramendi_, Jun 09 2015
%H A180201 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A180201 a(n) = A233280(A258746(n)) = A117120(A233280(n)), n > 0. - _Yosu Yurramendi_, Apr 10 2017 [Corrected by _Yosu Yurramendi_, Mar 14 2025]
%F A180201 a(0) = 0, a(1) = 1, for n > 0 a(2*n) = 2*a(n) + [n even], a(2*n + 1) = 2*a(n) + [n odd]. - _Yosu Yurramendi_, May 23 2020
%F A180201 From _Alan Michael Gómez Calderón_, Mar 04 2025: (Start)
%F A180201 a(n) = A054429(n) XOR floor(n/2) for n > 0.
%F A180201 a(n) = A054429(A003188(n)) for n > 0. (End)
%F A180201 a(n) = A154436(A054429(n)), n > 0. - _Yosu Yurramendi_, Mar 11 2025
%o A180201 (R)
%o A180201 #
%o A180201 maxn <- 63 # by choice
%o A180201 a <- 1
%o A180201 for(n in 1:maxn){
%o A180201 a[2*n  ] <- 2*a[n] + (n%%2 == 0)
%o A180201 a[2*n+1] <- 2*a[n] + (n%%2 != 0)}
%o A180201 a <- c(0, a)
%o A180201 # _Yosu Yurramendi_, May 23 2020
%K A180201 nonn,easy
%O A180201 0,3
%A A180201 _Reinhard Zumkeller_, Aug 15 2010